Oleg Ledeniov, Shaul Markovitch
The utility problem occurs when the cost of the acquired knowledge outweighs its benefits. When the learner acquires control knowledge for speeding up a problem solver, the benefit is the speedup gained due to the better control, and the cost is the added time required by the control procedure due to the added knowledge. Previous work in this area was mainly concerned with the costs of matching control rules. The solutions to this kind of utility problem involved some kind of selection mechanism to reduce the number of control rules. In this work we deal with a control mechanism that carries very high cost regardless of the particular knowledge acquired. We propose to use in such cases explicit reasoning about the economy of the control process. The solution includes three steps. First, the control procedure must be converted to anytime procedure. Second, a resource-investment function should be acquired to learn the expected return in speedup time for additional control time. Third, the function is used to determine a stopping condition for the anytime procedure. We have implemented this framework within the context of a program for speeding up logic inference by subgoal ordering. The control procedure utilizes the acquired control knowledge to find efficient subgoal ordering. The cost of ordering, however, may outweigh its benefit. Resource investment functions are used to cut-off ordering when the future net return is estimated to be negative.